On-chip photodetection of angular momentums of vortex structured light

Structured vortex light with orbital angular momentum (OAM) shows great promise for high-bandwidth optical communications, quantum information and computing, optical tweezers, microscopy, astronomy, among others. Generating, controlling, and detecting of vortex light by all-electrical means is at the heart of next generation nanophotonic platforms. However, on-chip electrical photodetection of structured vortex light remains challenging. Here, we propose an on-chip photodetector based on 2D broadband thermoelectric material (PdSe2) with a well-designed spin-Hall couplers to directly characterize angular momentum modes of vortex structured light. Photothermoelectric responses in the PdSe2 nanoflake, excited by the focusing surface plasmons, show a magnitude proportional to the total angular momentum modes of the infrared vortex beams, thereby achieving direct detection of spin and orbital angular momentum, as well as the chirality and ellipticity of scalar vortex lights. Our works provide a promising strategy for developing on-chip angular momentum optoelectronic devices, which play a key role in the next-generation high-capacity optical communications, quantum information and computing, imaging, and other photonic systems.


Supplementary Note 1: Design of the spin-Hall plasmonic coupler
The spin-Hall plasmonic coupler is designed based on two hierarchical structures as shown in Supplementary Figure 1.Particularly, the primary structure is a chiral plasmonic couplers made of two column apertures according to previous work 1 .
Firstly, we consider the surface plasmonic polariton (SPP) launched at the air-gold interface by a single aperture.The SPP wave vector can be calculated by: where, k0 is the wave vector of free space incident light, εair and εAu are dielectric constants of air and metal Au.The wavelength of SPP is calculated by   = 2   for the operation wavelength of 8 μm.As shown in Supplementary Figure 2, with well-designed geometric structure parameters, the single aperture launches the SPP with a wavelength   ≅ 8 μm, which agrees well with the theory.On the other hand, the single aperture shows a resonance extinction peak at λ = 8 μm.
Secondly, the apertures are arranged into two columns with appropriate geometric structure parameters as shown in Supplementary Figure 1.When the lateral spacing S of the columns is set to be S =  2   −1 , the SPP field intensities propagating to the right (IR) and the left (IL) to the pair of columns can be calculated by: where, E1 and E2 denote the amplitudes of the field components coupled to the respective columns and δ denotes the relative phase between the E1 and E2.As a result, the chiral plasmonic coupler made up of five column pairs can launch a unidirectional SPP wave under the illumination of circularly polarized light, as shown in Supplementary Figures 3 and 4.
Thirdly, when the chiral plasmonic couplers are bent into a semi-ring shape, the SPP can be tracked based on the Huygens-Fresnel principle 2 .As shown in 3 Supplementary Figure 1c, considering that the incident light has an electric field of  =  (+ℓ) ( ⃗  +  ⃗  ) with a circularly polarization state, the electric field at the surface is given by: where, j = σ+ ℓ is the total optical angular momentum modal index.By employing the paraxial approximation, the position at the peak focal point can be analytically expressed by: where,   is the first non-null zero point of the derivative of electric field distribution along x-direction.This means that the focal positions are totally determined by the optical angular momentum modal index j and the wavelength λSPP of SPPs.fringes reveal the absolute value and sign of the topological charge accordingly (Supplementary Figure 10).

4 Supplementary Figure 1 |
Design principle of the spin-Hall plasmonic coupler for sorting various angular momentum states.a, The primary chiral plasmonic couplers are bent into semi-ring shape to form the final hierarchical structures, which is used for sorting various superposed angular-momentum states including the spin and the orbital angular momentums.b, The chiral plasmonic coupler is made of column pairs spaced by λSPP.Two columns of apertures are positioned in parallel with spacing S. The columns couple to the field components E1 and E2 of the incident field E. The resulting SPP plane waves propagate to the right and the left side away from the column pair with intensities IR and IL.c, Mechanism of the sorting of the semi-ring-shaped grating.The  ⃗⃗ is the position vector of any point on a semi-ring slit,  ⃗ denotes the position vector of any viewpoint F. launched by multiple concentrically ringed column pairs.a,b, Simulated electric field of SPP (normalized by electric field of the incident light) above a coupler made up of four concentrically ringed column pairs under illumination by a plane wave with the right σ -(a) and the left σ + (b) circular polarization states.